oc2S {RBesT} | R Documentation |
Operating Characteristics for 2 Sample Design
Description
The oc2S
function defines a 2 sample design (priors, sample
sizes & decision function) for the calculation of operating
characeristics. A function is returned which calculates the
calculates the frequency at which the decision function is
evaluated to 1 when assuming known parameters.
Usage
oc2S(prior1, prior2, n1, n2, decision, ...)
## S3 method for class 'betaMix'
oc2S(prior1, prior2, n1, n2, decision, eps, ...)
## S3 method for class 'normMix'
oc2S(
prior1,
prior2,
n1,
n2,
decision,
sigma1,
sigma2,
eps = 1e-06,
Ngrid = 10,
...
)
## S3 method for class 'gammaMix'
oc2S(prior1, prior2, n1, n2, decision, eps = 1e-06, ...)
Arguments
prior1 |
Prior for sample 1. |
prior2 |
Prior for sample 2. |
n1 , n2 |
Sample size of the respective samples. Sample size |
decision |
Two-sample decision function to use; see |
... |
Optional arguments. |
eps |
Support of random variables are determined as the
interval covering |
sigma1 |
The fixed reference scale of sample 1. If left unspecified, the default reference scale of the prior 1 is assumed. |
sigma2 |
The fixed reference scale of sample 2. If left unspecified, the default reference scale of the prior 2 is assumed. |
Ngrid |
Determines density of discretization grid on which decision function is evaluated (see below for more details). |
Details
The oc2S
function defines a 2 sample design and
returns a function which calculates its operating
characteristics. This is the frequency with which the decision
function is evaluated to 1 under the assumption of a given true
distribution of the data defined by the known parameter
\theta_1
and \theta_2
. The 2 sample design is defined
by the priors, the sample sizes and the decision function,
D(y_1,y_2)
. These uniquely define the decision boundary , see
decision2S_boundary
.
Calling the oc2S
function calculates the decision boundary
D_1(y_2)
(see decision2S_boundary
) and returns
a function which can be used to calculate the desired frequency
which is evaluated as
\int f_2(y_2|\theta_2) F_1(D_1(y_2)|\theta_1) dy_2.
See below for examples and specifics for the supported mixture priors.
Value
Returns a function which when called with two arguments
theta1
and theta2
will return the frequencies at
which the decision function is evaluated to 1 whenever the data is
distributed according to the known parameter values in each
sample. Note that the returned function takes vector arguments.
Methods (by class)
-
oc2S(betaMix)
: Applies for binomial model with a mixture beta prior. The calculations use exact expressions. If the optional argumenteps
is defined, then an approximate method is used which limits the search for the decision boundary to the region of1-eps
probability mass. This is useful for designs with large sample sizes where an exact approach is very costly to calculate. -
oc2S(normMix)
: Applies for the normal model with known standard deviation\sigma
and normal mixture priors for the means. As a consequence from the assumption of a known standard deviation, the calculation discards sampling uncertainty of the second moment. The function has two extra arguments (with defaults):eps
(10^{-6}
) andNgrid
(10). The decision boundary is searched in the region of probability mass1-eps
, respectively fory_1
andy_2
. The continuous decision function is evaluated at a discrete grid, which is determined by a spacing with\delta_2 = \sigma_2/\sqrt{N_{grid}}
. Once the decision boundary is evaluated at the discrete steps, a spline is used to inter-polate the decision boundary at intermediate points. -
oc2S(gammaMix)
: Applies for the Poisson model with a gamma mixture prior for the rate parameter. The functionoc2S
takes an extra argumenteps
(defaults to10^{-6}
) which determines the region of probability mass1-eps
where the boundary is searched fory_1
andy_2
, respectively.
References
Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics 2014;70(4):1023-1032.
See Also
Other design2S:
decision2S_boundary()
,
decision2S()
,
pos2S()
Examples
# example from Schmidli et al., 2014
dec <- decision2S(0.975, 0, lower.tail=FALSE)
prior_inf <- mixbeta(c(1, 4, 16))
prior_rob <- robustify(prior_inf, weight=0.2, mean=0.5)
prior_uni <- mixbeta(c(1, 1, 1))
N <- 40
N_ctl <- N - 20
# compare designs with different priors
design_uni <- oc2S(prior_uni, prior_uni, N, N_ctl, dec)
design_inf <- oc2S(prior_uni, prior_inf, N, N_ctl, dec)
design_rob <- oc2S(prior_uni, prior_rob, N, N_ctl, dec)
# type I error
curve(design_inf(x,x), 0, 1)
curve(design_uni(x,x), lty=2, add=TRUE)
curve(design_rob(x,x), lty=3, add=TRUE)
# power
curve(design_inf(0.2+x,0.2), 0, 0.5)
curve(design_uni(0.2+x,0.2), lty=2, add=TRUE)
curve(design_rob(0.2+x,0.2), lty=3, add=TRUE)